#### Answer

$t-5$

#### Work Step by Step

When subtracting two fractions with common denominators, we subtract the numerators and copy the denominator. Therefore, the given expression, $
\dfrac{t^2}{t-3}-\dfrac{8t-15}{t-3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{t^2-(8t-15)}{t-3}
\\\\=
\dfrac{t^2-8t+15}{t-3}
\\\\=
\dfrac{(t-5)(t-3)}{t-3}
\\\\=
\dfrac{(t-5)(\cancel{t-3})}{\cancel{t-3}}
\\\\=
t-5
.\end{array}